Question

If sin A =9/41, Compute Cos A and tan A

Answer 1

Sin A = Opp. side/ Hypotenuse = 9/41

by using Pythagoras theorem,

a²+b² = c²
(9)² + b² = (41)²
b² = 1681-81
b² = 1600
b = 40

Cos A = Adj./Hyp. = 40/41
Tan A = Opp./Adj. = 9/40.

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Answer 2

$\cos A=\dfrac{40}{41}$ and $\tan A=\dfrac{9}{40}$

Step-by-step explanation:

We have,

$\sin A=\dfrac{9}{41}$

To find, $\cos A$ and$\tan A$=?

$\sin A=\dfrac{9}{41}=\dfrac{p}{h}$

By Pythagoras theorem,

$b=\sqrt{h^{2}-p^{2} }$

$b=\sqrt{41^{2}-9^{2}}=\sqrt{1681-81}=\sqrt{1600} =40$

Where, h = hypotenuse, p = perpendicular and b = base

∴ $\cos A=\dfrac{b}{h} =\dfrac{40}{41}$ and

$\tan A=\dfrac{p}{b} =\dfrac{9}{40}$